Bulk queue model with two phase’s service, unreliable server and m phase of repair

Ashu Vij¹

1. Department of Mathematics, DAV College, Amritsar, India.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.3 , pp.111-124, Jun-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.111124

Online published on Jun 30, 2018

Copyright © Ashu Vij . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In the present investigation, we have considered state dependent unreliable bulk queueing model with two phase of service and m phase of repair. The server provides first phase of service to each arriving unit while second phase is optional, provided as per demand of the unit. The server is subject to breakdown at any instant of services; whenever the server gets break down during the service (any phase), then it is immediately send for repair. The repair of server done in m different phases. We obtain the steady state queue size distribution in explicit and closed form in terms of the probability generating functions for the number of customers in the queue. Various performance indices viz. average number of customers in queue and system, long run probabilities of server being in different states, availability, mean time to failure etc. Some special cases of interest are discussed by setting appropriate parameters. To validate the analytical results, numerical results are obtained by taking an illustration.

Key-Words / Index Term :
Queue, Bulk, Essential service, Optional service, Supplementary variable, Server break down, Queue length

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